Question

The volume of a right cone is 3,696 m' and its height is 18 m. Find the following for the cone
(a) lateral surface area
(b) total surface area
5. The curved surface area of a right cone is 440 m and its slant height is 14 m. Find the following for​

Answer 1

Answer:

formula of right circular cone =πr(l+r)

Answer 2

$\bold{\underline{\underline{\huge{\sf{ANSWER\:4:}}}}}$

Given:

The volume of a right cone is 3696m³ and it's height is 18m.

To find:

• Lateral surface area.

• Total surface area.

Explanation:

We have,

The volume of the right circular cone= 3696m³.

We know that formula of the volume of cone: $\frac{1}{3}$πr²h

→ $\frac{1}{3} *\frac{22}{7} *r^{2} *18m=\:3696m^{3}$

→ $\frac{22}{21} *r^{2} *18m=3696m^{3}$

→ r² = $(\frac{3696*18*21}{22} )m$

→ r² =$\frac{\cancel{3696}*18*21}{\cancel{22}}$

→ r² = (168×18×21)m

→ r² = 63504m

→ r = √63504m

→ r = 252m

∴Slant height,l= √r²+h²

Therefore,

Formula of the lateral surface area of cone: πrl

→ $\frac{22}{7} *252*\sqrt{252^{2} +18^{2} }$

→ $\frac{22}{\cancel{7}}*\cancel{252}*\sqrt{63504+324} }$

→ (22×36×252.64)m²

→ 200092.49m².

We know that total surface area of the cone: πr(l+r)     [sq.units]

→ $\frac{22}{\cancel{7}} *\cancel{252}*(252.64+252)m^{2}$

→ (22× 36×504.64)m²

→ 399674.88m².

$\bold{\underline{\underline{\huge{\sf{ANswer\:5:}}}}}$

Given:

The curved surface area of a right xone is 440m and it's slant height is 14m.

To find:

The radius of the base.

Explanation:

We know that formula of the curved surface area of cone: πrl

→ πrl =440m²

→ $\frac{22}{7} *r*14m=440m^{2}$

→ $\frac{22}{\cancel{7}} *r*\cancel{14}m=440m^{2}$

→ 22 × r ×2 =440

→ 44m× r= 440m²

→ r= $\cancel{\frac{440m^{2} }{44m} }$

→ r= 10m

Thus,

The radius of the base is 10m.